Determining the bubble nucleation efficiency of low-energy nuclear recoils in superheated C3 F8 dark matter detectors

The bubble nucleation efficiency of low-energy nuclear recoils in superheated liquids plays a crucial role in interpreting results from direct searches for weakly interacting massive particle (WIMP) dark matter. The PICO collaboration presents the results of the efficiencies for bubble nucleation from carbon and fluorine recoils in superheated C3F8 from calibration data taken with five distinct neutron spectra at various thermodynamic thresholds ranging from 2.1 to 3.9 keV. Instead of assuming any particular functional forms for the nuclear recoil efficiency, a generalized piecewise linear model is proposed with systematic errors included as nuisance parameters to minimize model-introduced uncertainties. A Markov chain Monte Carlo routine is applied to sample the nuclear recoil efficiency for fluorine and carbon at 2.45 and 3.29 keV thermodynamic thresholds simultaneously. The nucleation efficiency for fluorine was found to be ≥50% for nuclear recoils of 3.3 keV (3.7 keV) at a thermodynamic Seitz threshold of 2.45 keV (3.29 keV), and for carbon the efficiency was found to be ≥50% for recoils of 10.6 keV (11.1 keV) at a threshold of 2.45 keV (3.29 keV). Simulated datasets are used to calculate a p value for the fit, confirming that the model used is compatible with the data. The fit paradigm is also assessed for potential systematic biases, which although small, are corrected for. Additional steps are performed to calculate the expected interaction rates of WIMPs in the PICO-60 detector, a requirement for calculating WIMP exclusion limits.